MA 3972-MA-Book April 11, 2018 16:20
AP Calculus AB Practice Exam 2 379
- Iff(x)=5 cos^2 (π−x), then f′
(
π
2
)
is
(A) 0 (B) − 5
(C) 5 (D) − 10
- g(x)=
∫x
1
3 t
t^3 + 1
dt, theng′(2) is
(A) 0 (B) −
2
3
(C)
2
3
(D)
5
6
- If
∫ 2
k
(2x−2)dx=−3, a possible value ofkis
(A) − 2 (B) 0
(C) 1 (D) 3
- If
∫a
0
f(x)dx=−
∫ 0
−a
f(x)dxfor all positive
values ofa, then which of the following could
be the graph off? (See below.)
y
0 x
y
0 x
(A) (B)
y
0 x
(C) y
0 x
(D)
- A functionfis continuous on [1, 5], and some
of the values offare shown below:
x 1 3 5
f(x) − 2 b − 1
Iff has only one root,r, on the closed inter-
val [1, 5], andr=3, then a possible value ofbis
(A) − 1 (B) 0
(C) 1 (D) 3
- Given the equationV=
1
3
πr^2 (5−r), what is
the instantaneous rate of change ofVwith
respect toratr=5?
(A) −
25 π
3
(B)
25 π
3
(C)
50 π
3
(D) 25π
- What is the slope of the tangent to the curve
x^3 −y^2 =1atx=1?
(A) 0 (B)
3
2
√
2
(C)
3
2
(D) Undefined
- The graph of functionfis shown below.
Which of the following is true forf on the
interval (a,b)? y
x
ab^0
f
I. The functionf is differentiable on (a,b).
II. There exists a numberkon (a,b) such
thatf′(k)=0.
III. f′′>0on(a,b).
(A) I only
(B) II only
(C) I and II only
(D) II and III only
- The velocity function of a moving particle on
thex-axis is given asv(t)=t^2 − 3 t−10. For
what positive values oftis the particle’s speed
increasing?
(A) 0<t<
3
2
only
(B) t>
3
2
only
(C) t>5 only
(D) 0<t<
3
2
andt>5 only
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